Role of turbulent shear stresses in particle dispersion

Abstract

Introduction T HE technological applications of combustion processes in many cases involve the use of two phase flows or sprays. A large number of other important industrial and physical processes make use of turbulent two phase flows. The calculation of these flows is not at all trivial, particularly if the sprays are dense and the turbulence is modulated by the particle phase. Several methods have been developed for the calculation of these flows. If the two phases are treated separately, then the stochastic simulation technique' has considerable attraction for the modeling of practical spray systems. In the stochastic simulation method a turbulence closure model is used to develop an Eulerian description of the turbulent flowfield. Statistics of the velocities at a single point in the flow are obtained from this calculation; these statistics include the means and the variances of the velocity components. If a Gaussian probability distribution function (PDF) for the velocity is assumed, in reasonable accord with available measurements, then a random number generator may be used to sample the PDF. With these velocity samples the position of particles may be advanced by integrating the particle equation of motion through the flowfield. The equation of motion is, in most cases, simply the equation for the rate of change of momentum due to the drag operating on the particle. In the case of a fluid particle, the motion is obtained by simply integrating the particle velocity to obtain updated particle positions. Many authors' have assumed that turbulent shear stresses do not play a role in the dispersion of particles in their stochastic simulations. However, there is no a priori justification for the omission of the shear stresses from stochastic, Lagrangian simulations of the type that have been discussed so far. Berlemont et al. have developed the most complete formulation of the particle dispersion problem, wherein they used a mathematical process to impose the correct correlations between the fluid velocity components. The correlations or turbulent shear stresses were obtained from an algebraic closure model. In addition, their approach was extended to include a realistic autocorrelation function for fluid velocity in contrast to the older methods of Shuen et al., who assumed that the